Generally, in computer graphics, objects are represented as surfaces, with the surfaces being represented by meshes at a particular level. A mesh at a particular consists of a set of vertices, or points in three-dimensional space, which are interconnected by edges. The edges define polygonal faces, which may be in the form of triangles, quadrilaterals, and so forth. In some computer graphic operations, it is desirable to generate a representation of a surface at a finer resolution than a current representation. There are several popular methodologies for generating a representation of a surface at a finer resolution than a current representation, including a Catmull-Clark surface subdivision methodology, which is used in connection with surfaces defined by a quadrilateral mesh, and a Loop surface subdivision methodology, which is used in connection with surface defined by a triangular mesh. Generally, both methodologies make use of respective subdivision rules at respective vertices defining the surface at a particular level in the mesh to generate a mesh in a next higher subdivision level. The surface of the respective object, which is referred to as the “subdivision surface” or “limit surface,” is taken as being defined by a mesh as the subdivision level approaches infinity.
A feature on a subdivision surface can be defined by a feature line in the mesh that defines the respective surface. A feature line can be in the form of a sharp crease or a smooth curve. For a smooth feature line, a normal vector, which is the vector that is perpendicular to a plane that is tangent to the surface, will vary continuously across the smooth feature line. On the other hand, for a sharp crease, the normal vector varies discontinuously across the crease, and in fact is not defined at the crease. However, a definition for a smooth curve can be derived from a definition for a sharp crease using one or more parameters that are used to define the sharpness of the curve across vertices in the mesh at a particular subdivision level. D. Zorin, “Stationary Subdivision And Multi-Resolution Surface Representation,” Ph.D. Thesis, California Institute of Technology, Pasadena, Calif., 1998, describes a methodology for generating a smooth feature line using parameters, but the methodology described there results in surfaces of relatively low quality, even in surfaces that are not smooth at some vertices in the surface topology. T. DeRose, et al., “Subdivision surfaces in character animation,” SIGGRAPH 98 Conference Proceedings, Annual Conference Series, pages 85-94, ACM SIGGRAPH, 1998, describes a methodology for generating a smooth feature line based on applying a subdivision rule corresponding to sharp creases, as described in H. Hoppe, et al., “Piecewise Smooth Surface reconstruction,” SIGGRAPH 94 Conference Proceedings, Annual Conference Series, ACM SIGGRAPH, 1994, up to a selected fineness level, and a rule corresponding to smooth interior points thereafter. Applying the two distinctly different types of rules makes efficient evaluation of the resulting surface difficult.